
theorem
  2897 is prime
proof
  now
    2897 = 2*1448 + 1; hence not 2 divides 2897 by NAT_4:9;
    2897 = 3*965 + 2; hence not 3 divides 2897 by NAT_4:9;
    2897 = 5*579 + 2; hence not 5 divides 2897 by NAT_4:9;
    2897 = 7*413 + 6; hence not 7 divides 2897 by NAT_4:9;
    2897 = 11*263 + 4; hence not 11 divides 2897 by NAT_4:9;
    2897 = 13*222 + 11; hence not 13 divides 2897 by NAT_4:9;
    2897 = 17*170 + 7; hence not 17 divides 2897 by NAT_4:9;
    2897 = 19*152 + 9; hence not 19 divides 2897 by NAT_4:9;
    2897 = 23*125 + 22; hence not 23 divides 2897 by NAT_4:9;
    2897 = 29*99 + 26; hence not 29 divides 2897 by NAT_4:9;
    2897 = 31*93 + 14; hence not 31 divides 2897 by NAT_4:9;
    2897 = 37*78 + 11; hence not 37 divides 2897 by NAT_4:9;
    2897 = 41*70 + 27; hence not 41 divides 2897 by NAT_4:9;
    2897 = 43*67 + 16; hence not 43 divides 2897 by NAT_4:9;
    2897 = 47*61 + 30; hence not 47 divides 2897 by NAT_4:9;
    2897 = 53*54 + 35; hence not 53 divides 2897 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2897 & n is prime
  holds not n divides 2897 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
